please show the answers without work clearly
please show the answers without work clearly Minimize g = 3a5y Subject to 4x + y...
8 Minimize z= x + 3y 9 + 22 54 + 4yΣ Subject to 2y + 2 > ΛΙ ΛΙ ΛΙΛΙ ΛΙ 14 O Σ Ο Minimum is Maximize z = 4x + 2y 32 + 4y < < 32 5x + 5y < Subject to 0 VI VI ALAI y 0 Maximum is
10. What is the dual of the following problem: Minimize x1 + x2, subject to xi 20, x2 > 0, 2xı > 4, x1 + 3x2 > 11? Find the solution to both this problem and its dual, and verify that minimum equals maximum.
[1.38] Consider the problem: Minimize cx subject to Axb, x>0. Suppose that one component of the vector b, say bị, is increased by one unit to b; + 1. a. What happens to the feasible region? b. What happens to the optimal objective value?
Consider the following minimum problem: Minimize: C = 22 Subject to the constraints: 1 +5:03 > 10 -621 +5x2 > 3 X>0 22 > 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P= (Select) Y1+ (Select) Y2 [ Select) Y1+ (Select) Y2 50 (Select) Yi+ 10 Y2 <1 yı >0; 92 > 0
(10pts) 3. Use direct proof to show that if x and y are positive real numbers, then (x+y)" > " + y".
Solve the linear programming problem 91 minimize w = 40J1 + 3092 + 20J3 + 1094 + 1095 J1 +293 +44 > 300 subject to yi +42 +295 400 +244 +Js > 1000 91,..., J5 20 ΛΙΛΙ ΛΙ 292
Solve the linear programming problem by simplex method. . Minimize C= -x - 2y + z. subject to 2x + y +2 < 14 4x + 2y + 3z < 28 2x + 5y + 5z < 30 x = 0, y>02 > 0
2. Show that for > 0, we have x4 + IV
Consider the following minimum problem: Minimize: C=2.01 +32 Subject to the constraints: 5.21 +22 > 9 201 + 2.02 > 10 > 0 * > 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P= (Select) Yi+ (Select) Y2 (Select) 31+ [ Select) y2 <2 (Select) Y1+ Select) y2 <1 yı > 0 y2 > 0
5. Given y,-t is a solution of t2y" + 2t1-2y = 0, for t > 0, find a second solution y2.